The aim of this work was to develop a novel phantom that supports the construction of highly reproducible phantoms with arbitrary activity distributions for PET imaging. It could offer a methodology for answering questions related to texture measurements in PET imaging. The basic idea is to move a point source on a 3-D trajectory in the field of view, while continuously acquiring data. The reconstruction results in a 3-D activity concentration map according to the pathway of the point source. A 22Na calibration point source was attached to a high precision robotic arm system, where the 3-D movement was software controlled. 3-D activity distributions of a homogeneous cube, a sphere, a spherical shell and a heart shape were simulated. These distributions were used to measure uniformity and to characterize reproducibility. Two potential applications using the lesion simulation method are presented: evaluation in changes of textural properties related to the position in the PET field of view; scanner comparison based on visual and quantitative evaluation of texture features. A lesion with volume of 50x50x50 mm3 can be simulated during approximately 1 hour. The reproducibility of the movement was found to be >99%. The coefficients of variation of the voxels within a simulated homogeneous cube was 2.34%. Based on 5 consecutive and independent measurements of a 36 mm diameter hot sphere, the coefficient of variation of the mean activity concentration was 0.68%. We obtained up to 18% differences within the values of investigated textural indexes, when measuring a lesion in different radial positions of the PET field of view. In comparison of two different human PET scanners the percentage differences between heterogeneity parameters were in the range of 5-55%. After harmonizing the voxel sizes this range reduced to 2-16%. The general activity distributions provided by the two different vendor show high similarity visually. For the demonstration of the flexibility of this method, the same pattern was also simulated on a small animal PET scanner giving similar results, both quantitatively and visually. 3-D motion of a point source in the PET field of view is capable to create an irregular shaped activity distribution with high reproducibility.